Three women, Roshel, Tammy and Irene went on a shopping spree. 30% of Roshel's spending was equal to ¹₂ of Tammy's spending. Irene's spending was  25% less than Tammy's. If Tammy spent $270 less, she would spend the same amount of money as Irene.

1. Find the ratio of Roshel's spending to Tammy's to Irene's.
2. How much did Irene spend?

Roshel	Tammy	Irene
5x4	3x4
	4x3	3x3
20 u	12 u	9 u

(a)
30%= ³⁰₁₀₀ = ³₁₀
³₁₀ of Roshel's spending is equal to ¹₂ of Tammy's spending. Make the numerators the same.  LCM of 3 and 1 is 3.

310 of Roshel's spending = 12 of Tammy's spending
310 of Roshel's spending =1x32x3 of Tammy's spending
310 of Roshel's spending = 36 of Tammy's spending

Roshel : Tammy
10 : 6
5 : 3

Irene's spending in percent when compared to Tammy's
= 100% - 25%
= 75%

Tammy : Irene
100 : 75
4 : 3

Tammy's spending is the repeated identity.  Make Tammy's spending the same.  LCM of 3 and 4 is 12.

Roshel : Tammy : Irene
20 : 12 : 9

(b)

	Roshel	Tammy	Irene
Before	20 u	12 u	9 u
Change		- 3 u
After	20 u	9 u	9 u

Additional amount that Tammy would have to spend less to be the same as Irene
= 12 u - 9 u
= 3 u

3 u = 270

1 u = 270 ÷ 3 = 90

Amount that Irene spent
= 9 u
= 9 x 90
= $810 

Answer(s): (a) 20 : 12 : 9; (b) $810